Please don't be put off by the circuit board requirement, I have listed it on kitspace such that it is really easy and cheap to get one: https://kitspace.org/boards/github.com/ozel/diy_particle_det... Even if you have never ordered a PCB, it should be straight forward using kitspace as a proxy to get it right.
For beginners, I would propose soldering the electron-detector first (on the plus side, it has 4 times more the sensitivity) and if that works swap few parts and upgrade to the alpha-spectrometer variant since that is a bit more tricky to operate and get running. I've commented on the through-hole/SMD choice and similar questions in this twitter thread https://twitter.com/0zelot/status/1260931205676990466.
In short, I choose leaded components over SMD where possible such that it is easy to solder. But analog signal integrity and low noise vs. signal require a circuit board.